Question

Which of the following are characteristics of the graph of the reciprocal parent function?

A. It has horizontal and vertical asymptotes.
B. It has one y-intercept.
C. It does not have intercepts.
D. It passes through the origin.

Answer 1

I said A because the horizontal and vertical they asymptotes

Answer 2

C. It does not have intercepts.

Explanation:

Reciprocal parent function is
`y=(1)/(x)`

which can also be seen as xy=1

now since x intercept requires y=0 and y intercept requires x=0 .

plugging x=0 gives 0=1

and plugging y=0 gives 0=1 again

which can never be true so there won't be any x-intercept or y-intercept.

Correct option is then C. It does not have intercepts.